Image classification via a quantum-inspired strategy involving a mixture of experts

Numerous studies have analyzed the use of hybrid quantum-classical convolutional neural networks as a promising alternative to classical deep learning. However, network components on quantum hardware impose fundamental limitations, while the scalability of quantum circuits leads to trainability issues. In this work, we investigate whether small, classically-emulated quantum circuit components can play a meaningful role within complex models, offering an alternative to purely classical convolutional architectures. To this end, we present a systematic study of the effectiveness of a Hybrid Quantum-inspired Convolutional Neural Network (HQiCNN) compared with a parameter-matched classical Convolutional Neural Network (CNN) that differs only in an intermediate dense neural layer. Both models are evaluated on two real-world medical datasets while systematically varying the different hyperparameters, ensuring a fair model comparison that is both dataset and hyperparameter independent. The results show that no architecture consistently dominates the other: the HQiCNN achieves its largest gains in intermediate-data regimes, whereas the CNN reaches the highest accuracies for the largest training sets in both datasets. Furthermore, removing entanglement produces comparable performance while enabling substantially better scalability of quantum simulations, and richer observable sets become beneficial only when sufficient training data are available. Finally, we propose two SHAP-based explainability tools for comparing the predictions between both models, $|SHAP|$IoU and $EMD_{pos}$ metric, to demonstrate that both architectures consistently attend to anatomically plausible regions. Thus, we provide a comprehensive benchmark showing that, under certain conditions, hybrid quantum-inspired models are an alternative that can offer benefits in practical tasks such as medical image classification.

We propose a method to optimize the correlation among convolutional neural network (CNN) features that are used as inputs to quantum neural network (QNN) to enhance image classification accuracy. Unlike prior approaches that employ orthogonal decomposition as preprocessing, we intentionally introduce correlated features that are more physically compatible with QNN. This design leverages the QNN's inherent ability to exploit quantum entanglement for representing correlated states-an advantage unavailable to classical neural networks. We hypothesize that aligning feature correlations with the entanglement structure of QNN improves binary classification performance. Based on a mathematical derivation of QNN outputs, Monte Carlo simulations indicate that an average correlation between features of 0.5 yields optimal classification accuracy. To validate this finding, we evaluate a quantum-classical hybrid model on three tasks: CIFAR-10 (automobile vs. truck), Fashion-MNIST (shirt vs. coat), and radar micro-Doppler signatures (robotic dogs vs. non-robots). To regulate feature correlations, we introduce a correlation-regularization term on the outputs of the CNN, driving the off-diagonal entries of the feature correlation matrix toward a target constant. Across all datasets, inducing intermediate correlation consistently improved accuracy compared to low, high, or unregulated correlations, while also reducing classification accuracy variance. These results demonstrate that imposing moderate feature correlations-without modifying the quantum circuit-enhances classification accuracy and stability by aligning feature statistics with the QNN's entanglement structure. This study highlights the potential of QNN to surpass the performance of classical classifiers as more qubits become available.

The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching $\sim$ 0.90 versus $\sim$ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers substantially superior parameter and memory efficiency, requiring $\sim$ 94% fewer parameters and $\sim$ 75% less memory than CCNN at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.